The formula this page uses
For a/b and c/d, the lowest common denominator is L = LCM(b, d). Then a/b = a × (L ÷ b) / L.
Find a common denominator for your fractions
Use the free common denominator calculator to work through the number relationship, preserve exact values, and check the result with estimation. Choose a focused operation below to calculate, inspect the method, and connect the result to a visual model.
The visual updates with your calculation.
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Show your work Step-by-step method
- The calculation method and verification will appear here.
Arithmetic
Common Denominator Calculator explained
The short version
- Two fractions can only be added, subtracted or lined up in order once their bottom numbers match.
- The lowest common denominator is just the least common multiple of the bottom numbers.
- Whatever you multiply a bottom by, multiply that fraction's top by the same amount.
What each part means
SymbolWhat it means
b and d — The two bottom numbersThe denominators you start with. They can be any whole numbers above 0.
L — The common denominatorA number both b and d divide into exactly. The smallest such number keeps the arithmetic light.
L ÷ b — The multiplierHow many times the old bottom fits into the new one. The top gets multiplied by this too.
equivalent fraction — The rewritten fractionDifferent digits, same value: 7/12 and 21/36 are the same amount.
Show your work: a full example
- Put 7/12 and 5/18 over one bottom7/12 and 5/18
- Break both bottoms into primes12 = 2 × 2 × 3 and 18 = 2 × 3 × 3
- Take the most of each primetwo 2s and two 3s, so L = 4 × 9 = 36
- Rewrite the first fraction36 ÷ 12 = 3, so 7/12 = 21/36
- Rewrite the second36 ÷ 18 = 2, so 5/18 = 10/36
- Now they can be compared21/36 is bigger than 10/36
- And added21/36 + 10/36 = 31/36
A second, different case
- A different case: three fractions, and one easy pair3/4, 1/6 and 5/9
- Break all three bottoms into primes4 = 2 × 2, 6 = 2 × 3, 9 = 3 × 3
- Take the most of each primetwo 2s and two 3s, so L = 36 again
- Rewrite all three3/4 = 27/36, 1/6 = 6/36, 5/9 = 20/36
- Put them in order6/36 < 20/36 < 27/36, so 1/6 < 5/9 < 3/4
- Now an easier pair2/5 and 7/15, where 15 is already a multiple of 5
- Only one side moves2/5 = 6/15, and 7/15 stays exactly as it is
Copy-ready example
7/12 and 5/18
Put 7/12 and 5/18 over one bottom
Questions about the Common Denominator Calculator
Do I have to use the lowest one?
No, any shared bottom gives a correct answer. Using 216 for twelfths and eighteenths works, and 7/12 + 5/18 comes out as 186/216, which reduces to 31/36. Choosing the lowest one just means you never have to do that reducing step.
Can I compare two fractions without a common bottom?
Yes, by cross-multiplying. For 7/12 against 5/18, compare 7 × 18 = 126 with 5 × 12 = 60, so 7/12 is bigger. This is fast for two fractions, but with three or more, rewriting them all over one bottom is far clearer.
What about fractions with letters on the bottom?
Same idea, using factors instead of numbers. For 1/x and 1/(x + 2), the shared bottom is x(x + 2), so the fractions become (x + 2)/x(x + 2) and x/x(x + 2). The multiplier is whatever the other bottom is.
Why does 15 and 20 give 60 rather than 300?
Because 15 and 20 share the factor 5. Multiplying them gives 300, which counts that 5 twice. The least common multiple keeps each prime just as many times as the greediest of the two bottoms needs, giving 2 × 2 × 3 × 5 = 60.
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Understand arithmetic behind this calculator
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GuidesLearn arithmeticConcepts, worked methods, and checks.
PracticePractice arithmetic questionsAnswer review after every attempt.
ReferenceArithmetic formulasConditions and examples for each formula.